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Finite element iterative solution of skin effect problems in open boundaries
Author(s) -
Aiello G.,
Alfonzetti S.,
Coco S.,
Salerno N.
Publication year - 1996
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/(sici)1099-1204(199601)9:1/2<125::aid-jnm232>3.0.co;2-z
Subject(s) - finite element method , convergence (economics) , boundary value problem , relaxation (psychology) , mathematical optimization , boundary (topology) , mathematics , iterative method , electrical conductor , current (fluid) , bounded function , boundary element method , computer science , mathematical analysis , physics , psychology , social psychology , quantum mechanics , economics , thermodynamics , economic growth
The paper proposes an iterative procedure, called current iteration, for the finite element solution of two‐dimensional steady‐state skin effect problems in open boundaries. In the procedure a fictitious boundary is introduced enclosing all the conductors. On it, the magnetic vector potential is first guessed and then iteratively updated according to the current density computed in the conductors. Conditions are obtained implying convergence to the exact solution of the unbounded problem whatever the initial guess. The choice of the fictitious boundary and the selection of the relaxation parameter in such a way that computational efficiency is obtained are discussed. The greatest advantage of the procedure is its ease of implementation in a pre‐existing finite element code for bounded problems. An axisymmetric version of the procedure is also described since implementation only involves minor changes as compared with the 2‐D one. Examples are provided in order to clarify and validate the procedure and compare it with other techniques.